Noether's theorem: Difference between revisions

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m Use <math>.
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\end{align}</math>
 
The first term in the brackets is the [[kinetic energy]] of the particle, while the second is its [[potential energy]]. Consider the generator of [[time translation]]s ''<math>Q'' = ''\frac{d''/''}{dt''}</math>. In other words, <math>Q[x(t)] = \dot{x}(t)</math>. The coordinate ''x'' has an explicit dependence on time, whilst ''V'' does not; consequently:
 
:<math>Q[L] =